A082150 A transform of C(n,2).
0, 0, 1, 9, 60, 360, 2040, 11088, 58240, 297216, 1480320, 7223040, 34636800, 163657728, 763549696, 3523645440, 16107110400, 73016672256, 328570011648, 1468890021888, 6528375193600, 28862235279360, 126993714118656
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-132,504,-1056,1152,-512).
Programs
-
GAP
List([0..23], n-> Binomial(n,2)*(2^(n-2)+4^(n-2))/2); # Muniru A Asiru, Feb 12 2018
-
Magma
[Binomial(n,2)*(2^(n-2) + 4^(n-2))/2: n in [0..30]]; // G. C. Greubel, Feb 10 2018
-
Maple
A082150:=[seq(binomial(n,2)*(2^(n-2)+4^(n-2))/2,n=0..23)]; # Muniru A Asiru, Feb 12 2018
-
Mathematica
CoefficientList[Series[(x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2, {x,0,50}], x] (* or *) Table[Binomial[n,2]*(2^(n-2) + 4^(n-2))/2, {n,0,30}] (* G. C. Greubel, Feb 10 2018 *) LinearRecurrence[{18,-132,504,-1056,1152,-512},{0,0,1,9,60,360},30] (* Harvey P. Dale, Jan 17 2022 *) -
Maxima
makelist(2^(n-4)*(2^(n-2)+1)*(n-1)*n, n, 0, 30); /* Bruno Berselli, Feb 13 2018 */
-
PARI
for(n=0,30, print1(binomial(n,2)*(2^(n-2) + 4^(n-2))/2, ", ")) \\ G. C. Greubel, Feb 10 2018
Formula
a(n) = C(n, 2)*(2^(n-2) + 4^(n-2))/2.
G.f.: (x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2.
G.f.: x^2*(36*x^3 - 30*x^2 + 9*x-1)/((1 - 2*x)^3*(4*x - 1)^3).
E.g.f.: x^2*exp(3*x)*cosh(x)/2.
From Bruno Berselli, Feb 12 2018: (Start)
E.g.f.: x^2*(1 + exp(2*x))*exp(2*x)/4.
a(n) = 2^(n-4)*(2^(n-2) + 1)*(n - 1)*n. (End)
Comments